Now, defining \(\mathbf {K}_{c, s}\)  as the \((c, s)\)  commutation matrix we have the following identity [1]}
\(\mathbf {vec}({\mathbf {X}}_i \otimes \mathbf {V}_i)= \left((\mathbf {I}_{d} \otimes \mathbf {K}_{c, s})(\mathbf {vec}({\mathbf {X}}_i) \otimes \mathbf {I}_c) \otimes \mathbf {I}_{s}\right)\mathbf {vec}(\mathbf {V}_i).\) 
